PHYS3671 Foundations of Physics 3C (2012/13)
12 lectures + 3 workshops in Michaelmas Term
Additional: Thermodynamics, an Engineering Approach Y.A. Cengel and M.A. Boles (McGraw-Hill Education 2nd revised Edition, 1997)
Syllabus: Revision of basic ideas, Heat, Zeroth law and temperature; Definition of state variables, forms of energy and chemical potential, the First Law; Heat engines and the Second law, Clausius inequality, Entropy and entropy change; Entropy change in reversible and non-reversible processes; Thermodynamic Potentials and Maxwell’s Relations; Availability of Energy and applications of entropy; Heat and refrigeration cycles; Equilibrium and phase transitions, Clausius-Clapeyron equation; Third law of thermodynamics, obtaining low temperatures; Thermodynamics in action; Basic postulates of statistical mechanics, micro/mactostates, distinguishable and indistinguishable particles, Stirling’s approximation, relationship to thermodynamics and entropy; Boltzmann distribution function; equipartition and the partition function; Bose-Einstein and Fermi-Dirac distribution functions, examples of 4He and electrons.
Condensed Matter Physics
18 lectures + 4 workshops in Michaelmas and Epiphany Term
Syllabus: Review of crystal structures and their description: periodic arrays, lattices and bases. Wave Diffraction and the Reciprocal Lattice: Braggʼs Law, scattered wave amplitude, Brillouin zones and structure factor. Crystal binding and Elastic Constants: Van der Waals solids, Ionic and covalent crystals, metals, elastic strains, compliance and stiffness. Phonons I: Crystal vibrations: Vibrations of a linear chain with one and two atom bases, quantization and phonons. Phonons II: Thermal properties: Phonon heat capacity, Einstein and Debye models, anharmonicity and thermal conductivity. The Drude model: an attempt to explain electrons as classical particles. Free Electron Fermi Gas Model: Energy levels, the Fermi-Dirac distribution, heat capacity, electrical and thermal conductivity of metals. Energy Bands: The nearly-free electron model, wave equation of an electron in a periodic potential, Bloch functions, Fermi surfaces, reduced and extended zone schemes. Bending of energy bands close to the Brillouin zone boundary: the effect of a periodic potential, effective masses, electrons and holes. Metals, Semimetals, Semiconductors and Insulators.
18 Lectures and 4 workshops in Epiphany Term
- Review of EM [Hecht Section 2.8, 3.2 and Appendix 1]
- Plane waves and spherical waves [Hecht Section 2.7 and 2.9]
- Fourier transforms: Linearity, convolution, shifting, scaling [Hecht Chapter 11]
- Propagating the solution to the wave equation using the angular spectral method [Goodman Chapter 3]
- Gaussian beams [Hecht Section 13.1]
- Near-field (Fresnel) and far-field (Fraunhofer) diffraction [Hecht Section 10.1 and 10.3]
- Simple cases: single and double slits [Hecht Section 10.1 and 10.2]
- Simple cases: multiple slits [Hecht Section 10.1 and 10.2]
- Phasors [Hecht Section 4.5 and 4.11]
- 2D diffraction: letters, and circular apertures [Hecht Section 10.2.3 and 10.3]
- Diffraction limit: Rayleigh criterion, Heisenberg microscope [Hecht Section 10.2]
- Spatial filtering [Hecht Section 13.2]
- Babinet’s Principle. Apodization [Hecht Section 10.3]
- Fabry Perot: Gaussian modes of a cavity [Hecht Section 9.6 and 13.1]
- Lasers and cavities [Hecht Section 13.1]
3 lectures in Easter Term, one by each lecturer
Lectures: 2 or 3 one-hour lectures per week.
Workshops: These provide an opportunity to work through and digest the course material by attempting exercises and assignments assisted by direct interaction with the lecturers and workshop leaders. Students will be divided into four groups, each of which will attend one one-hour class every two weeks.
Problem exercises: See http://www.dur.ac.uk/physics/students/problems/